3
(Â),.*-;rr (9) "=,*t, zr-zeu,r:\ -\ -5 : .(^) , (D) ,(Cy) e^) _ t R ;" h(x) : f (-x) : ii)lJL,Àr,urr htr"Lr ,,; (: f ' (x) , f (x) u)- h'(x) *i - t .l+lx; Jl*t SSt, h ;Jl+ll olr,:,. otiil ,4s1 - - bac 2OOi3 Oli :liJ'L".*il f (x) = (ax * b)e* * L æy;q l-2,+*1J.\r-Jtf ilj,rr.-r (O,i ,h sbr",+l-" j aJtJJ *;Çr J+Cr (Ç) , (Cf) a-rst * A(-l ,1) , u,J1 o9<, q,c b , a ü{,*Jt ù* 1 r . - e e A(-1, ,1) ,- ) L*LJI q2ç ,l.l-e JhJr .t, g(x) = -(x + l)e-' + 1, : i,!ÿJL:à;rçrl g -dtr)t )iâ(z . ;t*r e ulsia ÊLr" j aJIJJ ;Çl J[j.Jl (C n), l-2, + æ[ ** *, î,J;ji:ï î#,::, ;;l l .ÇÇtsl ù..,ü:^Uâr B ;U";r ai"ô J.i. (Ç) "-*tt ,l .r* - ê (Cr) ;-r.lt ;+i n:B:r^:tt s'(Â).rr*,ruJ,1....;ii -r h(x) = g@\:alyJu [-2,+ooIJÇJr*r,:ÿJr h arurr,;13 . h' (x) aiiiJl âJtJl *t(l t+l:; J+r trSa,h ütrJt ottij J9> cr", ( ç 0rri;aJ"L*Jl f (x) = e* - (3x + 1),;qLs R,L,>-n,r1 i:§..lt ülJl ):r(l (O ,i ,i),*rt-re uL"r rb Jl vr*!r "rf*Jl j;tJl r-A+ (Cf ) o<1, . ex - 3 ;rLlJ r X ;À+iÀl srJl ,qÀ *,9si. r oQ&uA +ua-uo o, ü;dt ,*^tFg0 atÀ,I ùi)d(Cf)"-^.t oi cr+.2 .*æ r- oo.r. n"*ir1,T,:;ï . r+rr.; Jlr+ J<" ÊJ,f ,Utr.tr ,p ,r,r1 ,rJ . a -oo rtea ÿ = -3x - 1 orl,t , (^) qru" t".ir* ü4 (?) "=;r oi .-*i . s (^) "ltqrq (C/) a*àe (C7) ;-rst e (A)6,"xn-rl. e g(x) = r'-=r*'- x * 1 , jtri.sR*t ;ÿ,rt g q,*"-rt ,Jull r&;( Ç (o,i, i),iÇ- r -b"" .- Jt -fi I j;]l,rj: tr"r(r?} ; ]-; ' rIl+.,,dro )u,FrrJ, "1.ô g(x) = 0 i.t,r,Jr,]c,*.3 . ldlr;i Je» J§r Êi ejlJt olr;: r,rri . a (g(a) x o,2o) (Cr) ,=,.r n-,1 s (-r i :.LlL* ô.Ji g(x) = e'(x + 3) ,:, RsLrÿ,rrgr arr,:r ,§1 i .limr-_* g(x) ,limr-1- g(x) = -\.t t+Ç; Jl.+ a'l ,;: g ülJl ôli-ij ot-it uùsi. 2 ] -0,80' - 0,7 gfuhJr,.p o rr-r )L,F g @) : 0 ;r"uJr oi i*,. 3 .x,,*=*g(x) "rr"l .t*14.éilrt .4 f (x) = -x * (x * 2) e x,.. R *t, 1\;- ott f ilrJr ùsJ - ( - 0, ï, î ) çtn r -L. r.r, JJ v**Jr g#r,J /aru ;çt .f+.,]r (Ç) *; . -oo -ric / iJrrir a,ç ü"r. i. r -oorro(Ç).a+"|5L-.-,ta ÿ: x clrt,.5rll (Â) *. ,'r ,i ir.r.,. .(Â)"a*tr pl a.Jq (C/)sjâiJt :.-:ru,)§j f (x) = ,' l- *L + (x * 2)] , .i L-y. +oo,-/ ,ilrrJr okr r,s. 2 /,.ttlr ot ;...1r',.u'\.f (x) =.g(X):;p:X ujg-r*§,fqi ù,a1 .j.i-j.3 .0 "a-ttor.iaLÂJr * (Cy) r-r"l (f) ,,LJl a.tot-.*si .s < f (a) = 7,34, u x -0,7 9 ). Èl*.rr ç (f), (^), (Cy) y,1. e c,t*àt rl : §.rUl 4r^dll JljJl # aJl,-," 1S ud<.l, t ,z; Cl :;J'LJI f (x) : ezx - 2 ex + 1 ,;;-tr *ir"rr 6).J[;qr-ort f i]lJr]ü,j f aJlJx.À-r,rr a;9s;.,* ( r . lro anJt.r;. -oo, *oo rrr iJIrJl .æ1( z . / :irrr.tr olr.i.: J9> Jsr, iJlJt ot ; oÇt ,rrri 1 3 .oLjlsll §.:t- g, (C) "-;.".tt ÿGi otjlsl ür ( a .ki*,j ,: "rLr û) .àtt jl i-tô Jî.i, (C) nçt "*çr oi g+i 1 S .(o,i ,i ).rtnsre rulr oÇr ,j (C) n-J n: /(1) , f(-1) *i1 r r.t*r (C*) ;,-;.:ts;l;i.g(x) = -f (x):aôuuR S,urJts urJrrrn(7 (c)* û?:il'L.*tt f (x) =## :aôr.rtD *,\r^ ill" f .(0 ,i ,h sl*Jl ,+LJl ,J,f!:Jr ,r*!r (C) u+, . f ut"l.iJ-r"rJt &r{+" ùs ( 1 : D s^ X JS Jri Cr" c,*-, b 9 4 ü,*+À- uJrs §r1 <il ir. 1 : f(x)="+fi .t{è-Jri arr{+..9* o/ aJlÀJl ètrt{, :. -i ( 3 . l+lx; Jp+ ,§.t f i.Jlr.tl olr;; ot*l ,,rcl( a . L{.J"l,. :,r}: cr*rLi" }j+jâd (C) tçr *:*+U ;ri dr- ( S f (-x) + f (x) = 2,D 6^ xJsJ*lc,.oic,*,(é . (C) "-^.lt Jr' (C) ,-r.lJ a,*Jt? ë;:Li lil." ( 7 0;? :U'L*Jl 1çfl = fi :ail'Jt' R 'rc:ÿJr /;Jr'rr d,s' .(0 ,i ,h ,.;ur. e utoa d- Jl v* l* nf âJIJJ jl.ll *=lr9 (C) . f ut"stcrtï-ije,rri( l (C),-".u * a S, lQ,)) ;r:,rr ol *1 2 O (O,i)ara.aJr r* (C) eUr ;-ru (Q ç*LJr alcr* g$ ( 3 g(x) =ï- *i- f @): a.à){,ru R,p:r,-orrgrarlJrù*r(4 g'(x) = ffi ,R,i"x6,.1"i dr.cji ü*1' . t€rxs Jsr+,-§ts g iJIrJl grFj Jr.+ 6;rr (.. R * g(x);,1:,J6ur (6 . (7) "r-;r, (C) ".i,!.*Jl ;,. :ll 6rurl( ; (C)tr'e--rç A(0, i),r",.rli riu ( r .(C);-u, (r):1,,f,,,: (.J4 :J.JL-""§-rt g(x)=e* +x *1 :ô/JtR.r.rirorrg aJtJl ,&i ÿ a.llrJl olrs r,rsi - r . r"-r» a3.;Jrræ .lim*-_*(g(x) - x - L) ;rç _ z ]-1,3 ,-7,2hçJr jcrr»e)l> g(x) = 0a.r"r..r; ,l i,*- ! .R *g(x) ;rL:,J6u-r,.j .(O,i,i).,.;lar"euLrl* e (Cg) ê;\ -t f (x) = #; 'a;ylu R ,rs :irJr / a.rr*l c,s,r 1 z . (o,.ï,j),jur eurca ab Jl vrJr çr*Jt + aJIJJ ;ul J-rJr (cf ) ./ uuroçsol-rr6urr p f' (x) = #&,R e^xJsJtic*n;l;.,--r f(a)'"tt*e;at; f@)=d+ 1 ,c,iù--: 4L-l,àJl sli i!;;Jt s (Ç) ;*r+ (D) .r,t tl al;tu ,.:*r - l (D) ltcJq r-r^11 tit",,.l;" V = .x .i1.1.-lt ".i [Â) -.;r.'^I ..1 ...,-z (Cy)^*rtrrJd o *oo .r^,, (C.)

18 Exercices Expo

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Page 1: 18 Exercices Expo

(Â),.*-;rr (9) "=,*t,

zr-zeu,r:\ -\ -5 :.(^) , (D) ,(Cy) e^) _ t

R ;" h(x) : f (-x) : ii)lJL,Àr,urr htr"Lr ,,; (:f ' (x) , f (x) u)- h'(x) *i - t

.l+lx; Jl*t SSt, h ;Jl+ll olr,:,. otiil ,4s1 - -bac 2OOi3 Oli :liJ'L".*il

f (x) = (ax * b)e* * L æy;q l-2,+*1J.\r-Jtf ilj,rr.-r(O,i ,h sbr",+l-" j aJtJJ *;Çr J+Cr (Ç) ,

(Cf) a-rst * A(-l ,1) , u,J1 o9<, q,c b , a ü{,*Jt ù* 1 r

. - e e A(-1, ,1) ,- (Ç ) L*LJI q2ç ,l.l-eJhJr .t, g(x) = -(x + l)e-' + 1, : i,!ÿJL:à;rçrl g -dtr)t )iâ(z

. ;t*r e ulsia ÊLr" j aJIJJ ;Çl J[j.Jl (C n), l-2, + æ[** *, î,J;ji:ï î#,::, ;;l l

.ÇÇtsl ù..,ü:^Uâr B ;U";r ai"ô J.i. (Ç) "-*tt ,l .r*

- ê(Cr) ;-r.lt ;+i n:B:r^:tt s'(Â).rr*,ruJ,1....;ii -r

h(x) = g@\:alyJu [-2,+ooIJÇJr*r,:ÿJr h arurr,;13. h' (x) aiiiJl âJtJl *t(l

t+l:; J+r trSa,h ütrJt ottij J9> cr", ( ç0rri;aJ"L*Jl

f (x) = e* - (3x + 1),;qLs R,L,>-n,r1 i:§..lt ülJl ):r(l(O ,i ,i),*rt-re uL"r rb Jl vr*!r "rf*Jl j;tJl r-A+ (Cf ) o<1,

. ex - 3 ;rLlJ r X ;À+iÀl srJl ,qÀ *,9si. r

oQ&uA +ua-uo o, ü;dt ,*^tFg0 atÀ,I ùi)d(Cf)"-^.t oi cr+.2

.*æ r- oo.r. n"*ir1,T,:;ï. r+rr.; Jlr+ J<" ÊJ,f ,Utr.tr ,p ,r,r1 ,rJ . a

-oo rtea ÿ = -3x - 1 orl,t , (^) qru" t".ir* ü4 (?) "=;r oi .-*i . s

(^) "ltqrq

(C/) a*àe c»

(C7) ;-rst e (A)6,"xn-rl. e

g(x) = r'-=r*'- x * 1 , jtri.sR*t ;ÿ,rt g q,*"-rt ,Jull r&;( Ç

(o,i, i),iÇ- r -b"" .- Jt -fi I j;]l,rj: tr"r(r?} ;

]-; ' rIl+.,,dro )u,FrrJ, "1.ô

g(x) = 0 i.t,r,Jr,]c,*.3. ldlr;i Je» J§r Êi ejlJt olr;: r,rri . a

(g(a) x o,2o) (Cr) ,=,.r n-,1 s(-r i :.LlL* ô.Ji

g(x) = e'(x + 3) ,:, RsLrÿ,rrgr arr,:r ,§1 i

.limr-_* g(x) ,limr-1- g(x) = -\.tt+Ç; Jl.+ a'l ,;: g ülJl ôli-ij ot-it uùsi. 2

] -0,80' - 0,7 gfuhJr,.p o rr-r )L,F g @) : 0 ;r"uJr oi i*,. 3

.x,,*=*g(x) "rr"l .t*14.éilrt .4

f (x) = -x * (x * 2) e x,.. R *t, 1\;-

ott f ilrJr ùsJ - ( -0, ï, î ) çtn r -L. r.r, JJ v**Jr g#r,J /aru ;çt .f+.,]r (Ç) *;

. -oo -ric / iJrrir a,ç ü"r. i. r

-oorro(Ç).a+"|5L-.-,ta ÿ: x clrt,.5rll (Â) *. ,'r ,i ir.r.,..(Â)"a*tr pl a.Jq (C/)sjâiJt :.-:ru,)§j .é

f (x) = ,' l- *L + (x * 2)] , .i L-y. +oo,-/ ,ilrrJr okr r,s. 2

/,.ttlr ot ;...1r',.u'\.f (x) =.g(X):;p:X ujg-r*§,fqi ù,a1 .j.i-j.3.0 "a-ttor.iaLÂJr * (Cy) r-r"l (f) ,,LJl a.tot-.*si .s

< f (a) = 7,34, u x -0,7 9 ). Èl*.rr ç (f), (^), (Cy) y,1. e

c,t*àt rl : §.rUl 4r^dll JljJl # aJl,-," 1S ud<.l, t ,z;

Cl :;J'LJI

f (x) : ezx - 2 ex + 1 ,;;-tr *ir"rr 6).J[;qr-ort f i]lJr]ü,j

f aJlJx.À-r,rr a;9s;.,* ( r

. lro anJt.r;. -oo, *oo rrr iJIrJl 4Ç .æ1( z

. / :irrr.tr olr.i.: J9> Jsr, iJlJt ot ; oÇt ,rrri 1 3

.oLjlsll §.:t- g, (C) "-;.".tt ÿGi Lô otjlsl ür ( a

.ki*,j ,: "rLr û) .àtt jl i-tô Jî.i, (C) nçt "*çr oi g+i

1 S

.(o,i ,i ).rtnsre rulr oÇr ,j (C) n-J n: /(1) , f(-1) *i1 r

r.t*r (C*) ;,-;.:ts;l;i.g(x) = -f (x):aôuuR S,urJts urJrrrn(7(c)*

û?:il'L.*tt

f (x) =## :aôr.rtD *,\r^ ill" f.(0 ,i ,h sl*Jl ,+LJl ,J,f!:Jr ,r*!r (C) u+,

. f ut"l.iJ-r"rJt &r{+" ùs ( 1

: D s^ X JS Jri Cr" c,*-, b 9 4 ü,*+À- uJrs §r1 <il ir. 1 :

f(x)="+fi.t{è-Jri arr{+..9* o/ aJlÀJl ètrt{, :. -i ( 3

. l+lx; Jp+ ,§.t f i.Jlr.tl olr;; ot*l ,,rcl( a

. L{.J"l,. :,r}: cr*rLi" }j+jâd (C) tçr *:*+U ;ri dr- ( S

f (-x) + f (x) = 2,D 6^ xJsJ*lc,.oic,*,(é. (C)

"-^.lt Jr' (C) ,-r.lJ a,*Jt? ë;:Li lil." ( 7

0;? :U'L*Jl

1çfl = fi :ail'Jt' R 'rc:ÿJr /;Jr'rr d,s'

.(0 ,i ,h ,.;ur. e utoa d- Jl v* l* nf âJIJJ jl.ll *=lr9 (C). f ut"stcrtï-ije,rri( l

(C),-".u * a S, lQ,)) ;r:,rr ol *1 2

O (O,i)ara.aJr r* (C) eUr ;-ru (Q ç*LJr alcr* g$ ( 3

g(x) =ï- *i- f @): a.à){,ru R,p:r,-orrgrarlJrù*r(4

g'(x) = ffi ,R,i"x6,.1"i dr.cji ü*1'

. t€rxs Jsr+,-§ts g iJIrJl grFj Jr.+ 6;rr (..

R * g(x);,1:,J6ur (6

. (7) "r-;r,

(C) ".i,!.*Jl

;,. :ll 6rurl( ;

(C)tr'e--rç A(0, i),r",.rli riu ( r

.(C);-u, (r):1,,f,,,:(.J4 :J.JL-""§-rt

g(x)=e* +x *1 :ô/JtR.r.rirorrg aJtJl ,&iÿ a.llrJl olrs r,rsi - r

. r"-r» a3.;Jrræ .lim*-_*(g(x) - x - L) ;rç _ z

]-1,3 ,-7,2hçJr jcrr»e)l> g(x) = 0a.r"r..r; ,l i,*- !

.R *g(x) ;rL:,J6u-r,.j

.(O,i,i).,.;lar"euLrl* e (Cg) ê;\ -t

f (x) = #; 'a;ylu R ,rs :irJr / a.rr*l c,s,r 1 z

. (o,.ï,j),jur eurca ab Jl vrJr çr*Jt + aJIJJ ;ul J-rJr (cf )

./ uuroçsol-rr6urr p f' (x) = #&,R e^xJsJtic*n;l;.,--r

f(a)'"tt*e;at; f@)=d+ 1 ,c,iù--:4L-l,àJl sli i!;;Jt s (Ç) ;*r+ (D) .r,t tl al;tu ,.:*r - l

(D) ltcJqr-r^11 tit",,.l;" V = .x .i1.1.-lt ".i [Â) -.;r.'^I ..1 ...,-z

(Cy)^*rtrrJd o

*oo .r^,, (C.)

Page 2: 18 Exercices Expo

11.'rri l1

rEÇ; Jrrz JS-r ri g llJlr$ ol,il ,r-,si ' 2

O,i,T)r"ç-exl*"f*,ll *r*.liq*-"Jr ; /u,r.r;Ul .ll$Jl (C1) e- i .çç,*, ,j*d*lL+iu.*il e.hôJé(CJ).*lrol c,-.-

:tr/)ru.*Jl gÇ,il1 ,(Cf)r--fq;»!l iriJlj^J:z-t ^ cm2 ^r*\ : :

.:,trètirl : rcUl ar-,Tt JlJ'lJl wà aJL., 18 t#<'rlJ lnÀn

!tL.lb:aJt*4J,

t1 :.i.J'U*Jt ig(x): (3 -Zx)e* *2 ';i:us R*t, ;a,')t§aJlJ1rd(i i ^ - {(') -

e2* -:' : '*,'':ÏU.T,,*îÏ',11L§'**i:ïï;îrl;ï), i (o,i,n,j'aesr*d-Jr vvrr,r#r.rarhrr;r..rru,' (9)r",,,, 1 t

. *oo r - * "u f aJlJl *.rl+ *i ' t

,,ï;:;e;=lQ";;, I iL-c.-iffiï,frï,1,,§;.-i:; ;i§ï: ;(r; ;;Ï.; i c:r,'|'"ù..-i"!"'-@'reqe(À) xr'r,,u"u;'- (c/) **"i t'r'3(A) Ê,ü*Jl , (Ç) *U a.Jl i"';eJl ,rrsi ' a

ex +4x-L h ., r -,. ,,

f (x) ='-i? :aôuLR,L:qr.rrl;.lt,ltr.;(y : atrl-.-u51.(A)+"*"ur5rr,(T)r.u"(C1)d!,-#oiix.i s

r(c1);-*l:: Jrëü.jl.iL.*ær- *u'f aJlJlo!Çel r : .(0,î'î) f§1,-À,/(Q)r(r)n-'J e

f' (x) ::!% :x uig>rs§"§1 g".j1 c+ii . , : JiÊ,*.1l elf)st*tl etlô Liir* m ÉL'i*ll L'"'l o+:*lÇt*"su' e

t :,'- (ex+L)' , .."=r-. - À- - É.. \. " : .ÿ = -x *m ' aJ't'J

f (a),à;*u'\;f (a) = 4a - 5:,iü*'3 ' 'r - '" '."1, .,,i -',

lJl/ ld..rt^-di. l+l,; J+a J(.:...;: / arUrr,;: oÇl ,'1si ' 4 i

.,.+îR.t"Y' .!*:iii'(aj*r,*,ra--,rq(C1)ur*!raâ,;eu{ri.6 i n(x) = -4+ (4-Zx)ex t h(x) = ex -2x

.oat-tÀJt sliilaiJl * (Cù a-r$(f; rt-r, iJrt".;51 ., i. .(O,i,Drjur.eut:. é*,f g aJIJJCçJl ,1ç^lr (Cr) c'+:

(c)r(A),(r),.)lse-,i .s i .R,r" h(x);;trl e^-rrh u"lt c,t ;:ol-l 'r'si

'l

:ajrt"!t JÈ;rLtle:s ?7I sÀ^iJl L.,'rl n*:*sÇt*,j;u'9 : '*oor-@*9 aJlrJl *;2Ç.Æi 'z

mex -4x *m*2 = 0 i .tel-FJlr+,-§:"t9 aJlrJl o1..;6lot-1 ,r,ri 3

l2:AJ'L*JI : .LSg < a 17,60:cæor+-r)l- g(x) =0a.r,r-"l,lc,*'a

f lr"r;çr.p"lr(f ,,(O,i,î)s,;t-*esLrer"^r'rrçg-Jl I R *g(x) ô'jL,:,lëP

h(x) =à' -**2:)an.F-sr,R.p:ir"rlha;"'ttlul,-(i : .ççdr.:+:Jr)-!.lima-affi ,li*r---(g(x) * 4)*i's.R*heJ[ll olr;;otjl r»rr1 .1 : "-'

x ,{^À>rs§,§l *h(x)> 3d,1ë,*r.,h-(0) ); i ,^{(? = ï=, ,- ,, .^ ,-,,"Ïlri;:i,Ï:i;|;

.tiç i#jJtri p.lima-1- [f(x) - (x * 1)] ' ùi ù*

i (Cr), i,.,üJt c,Ç.i:*!l glrt ,.rir:r r>. t+,rr- Jt+".so rc allrll ,*1+ =*-\ ':

f'(x): e-xh(x) :6!ir j"i-su§'§i .r"di rx.2 i .krr#Jlr+ lst t f allrJl ol.,"§ot-l ,4cl 'l

:(r),=+,: *,et,,-irlâr R,r,r..-r:,t- æ f (x) = 3.,i;ï,Jî ] I f @) ,",tt *E;ut,f (u) ='# ,,1i,*.,

I'r,te')t ia. I 'rt

Qy'l. *le éu3ÿ il'G TeJlàJl ùl ù-(Tr) rÉr-ucr.'.o É R c'.-rl : x * da:Jstorltr;''*'(T") us-t 6 i(T)

"r-*tl t-t- : .R * f alru i*r-lr JteJt ise17" 6;-l

. l*rl).-j Jl.z r.-rl d K ijlrjl ajr:-:" s ilrl ajlJl i'a'"-!'" JLüu1:l,a;t*;i i h(x) = (x - 1)e-* +2 :erhla!)rr!

^*:f',1::.Ï'.h iJtrJt .,l*; r,-r.l .

g(x)=*a"z(x-r) ,;!t"s R,r";\ro\1 9 àJlJl ,a-(i i ]-o,sa, -0,37[,e*,,.ü11-e]-,*h(x) - 0at.trt ,ij c,*

ÿ UlrJl o1,r; r,rri . f r -l. h(x) ;.,tr,1 e,"-t .

t 1 1l ,/-.\-^-,,o€ L-s'10],iæü,r»e)- J4g(x):0ar't'Jto'*' i Ctl élrf@) =2x*7-xe-* 'ôut Rl';i,Jrf iJlJlf,i(

R *g ti,l,léü-1.3 I Qcm n"Jull;oe). (O,ï,-D *Ç-r-u-d'"æaÇlt{#

f (x) = x2 + e\(x-t) :isyJr, R*r,alj*.lr:Jur/(v : f'(x): h(X) ' Rd,"xJ5J+i.r'ii'r\

\cm eJeulô§e). (0,i,î);Er"esur",'béeUrtt$(?)ss!' : ^ .4 '/ilrrrrot.,$'r

fo),f (i),r(-i),rr-1)'*1 1a i "'-l:*t::,'.1'',*.Ilt)sl \r) 'l \-r) 't \-4.,l:.Æ ' . rz \ 2a2+a-L.1 aL--r.ilr gri i-tâJlrr «:rl ** (Â) ot",, il,l., .-,si' - : f (a) = af '

oi *

upLrrd;!r "*e(Cùr(A)n-rr.e : qax -0,375 i;t) (C1) ;*stt(d)-ru.lto,;'-Jrr-ri

:m..ù,lqrjl ô§e). (O,i,j).,j1*raesura,'béeUl t$(Cf)c,s!, : 'f att'Jt ot';""iP -' :'

/rl, *,rr*.,J,j./'(x) =Zg(x),ra,lRg.i .lt^.j*, ü.al .ii,ü., : .+*'.(9),-r.lj.,3t^ v.»w ÿ =2x* 1:aj't'Jl ri(d)4'*"lt o1 r,*

Èl a-td C'1t72 :*\.t : .*fi-rsÿ*y =2X* p 'nrrU"n-;,-(ÂB)

r

y = o rx =2,x = \ I uçr*t} .ta,,rç(Cy),,-+t r*(ÂB)oÉ;-Êc*

I-+t- B - 0 :ÇHr il,t Jl Jy'-,* p,;;"tt L."rl Êf *ur'3tgx

Page 3: 18 Exercices Expo

c,l.àtirl : §cUl A:r,rTtl Jlrùjl ,,ÿà ArL*" iS l*d{ü lr*z;

l7:il'L*Jl

f (x):+ :-air".)tfurJr üs:t (.4

. (0,i ,ï) *q,, -L or* é;r..ir rur^* (Cy) ,i<.rr

[or + *[ s, f ut-,stol*,ii,,,l ; / ar"rr :"-;1.,,r.r . r

(C1) ;*st s»\.2C

1 ) q ^t;;;

M "^**1

AM u* ;-\ uL> r"_,ie ç1*Jr c," A ( 1 i 0) : r^ :rl1 r, 1u

.M zl";ltzt t"xu»uAM alL-Jt ù+.1

g(x) = (, - t)z *g# ,,g ,)t-,)t,tà.2

g (x) *t1 t

g" (x) = g2x + e-2* * 2,giù*1-. g -o)t"Jtol_r#r"rsl(

6

' ù1 ün*, ri: g' (x) :0 : .;i,.r R gr d *;i*p rs s2 o1 i,- ( s

.g'(x);rb,J6^:11e , 0,46 1a 10,47

. 0 r$r-ri c1 (c),n M":ü;rr * r* ": ;;."5;Ï,;. M o,t^^11 ,11, . ,

s(q) = lV{2")1, + lf @)1, t d - 1 = -lf {zo) :cJtù_ z

.2 x 70-2 ,.* AMo *'-at, g'ço1 J L* 6u-r;'lE:,il'LJt

f(x) = x + 2 - +:' =lwr;srr,R;,,rrorr /arr,.rrr,;Zcm n+ Jcut ;oe ). (O, i,7) ;t--, -ul r.l- ,,;r*rt ql+ (Ç) o+,

.-@r: /:.trr.rr or;ç *l .i. r. -oo r- (Cf )"="1 Ur" *-!tu ÿ = x + 2 -d't")t

e" (d) o"r-.;r oi c,*. :(d)

"r^-.1 +Jr, (C,/) , jàj+U:.: Jl a..;4r ,,r,i . n

f'(x) = tfi), :x ja;>ss§"|-rü. di.;t.i. z

. telxi] Jp+ JS.r e R *t :1,,rt / aJlJl ïjj ot*jt ,,;ri . -t ln3l-ulr et.;l;u;."rt eGi "-r"l(f çrLJr .pJea.ll ù<-r;u.i.3

(1") ; e.Jq (Cf ) i-.;e,,rrr , f ut.,stoç,: JLar. o1, = ;* + 1 ,e 0 iL-u.rr gt_i ila.âJl e (Cf),ur"l (Â) erLJr ürro, ù1 ü-.i . a

. (^) "a*;r

Jl qJri (Ç) "-.",r

i-;e,,rsi , ] -oo, ln 3] ;r*;r ,r,. -f " (x) = Vffi, * R,b ,a*rr f a",t f ', Çrrr u*Jr Jrr.-r üs.r )

(Cy) ;-l 'aru

;çr *n 1 : L;Jl ùi J+ô . s

(cr) , (^), (r), (d) r_,r l

ex.glx) =;r# :ô)uL R Jsiàrrttg i.|rui^t-'yt ajt.Jt ùi,.1.6»*tl .esJl ;elt oLu *r i-u!t ;-9 A (y). Uf.p JL Éqi- cs I gS.J. _

. x = 0 sx = T ;,.*t.ir-!le (d) "a*;r.

(e)._"qA(y) : 4ln 4 - ln@'r + z),c,,1dii_

.limr-_- A(y) *t.n

1zi:;J'l*J1

f (x) : x - #,;ur;iuR*r,,i-nrr /ar".tr ",;.(O,i,D *L5xui"f* 3l jqiJlrd+^i(C1) é*r:limr-_* f(x) , limr-+* f(x) . -i. r

.ot.r.ÜJr Jes *é.f' (x) > 0 :x;,;ss§.t-i i,.a;i g-.2a,ç.ru(42): ÿ = x - 1, (Â1): ÿ = x:-o*àr,Jl ü*FÀ-Jt ,l e.i.:

(a),(Âr ) oÇ.;.*;r, C I ^ !1,',,#,r"1.0 < a ( 0,5,e4*1ü, lq-e)l-,lraf (x) =0 iJ"GJt cri ù-.1.1

.eo +.J, = *,o,JèÈr.u.(c) *usr1(0, -]) o,*.,.,

. 0 u-ur û13 :L:Jl *i (Cf) ,*":t.rç (I) n+*.1 ar"u u,l . -.1 o = 0,45 *ù (Cf)t (Â2) , (Â1) ssr e

u, = l: @ - f (x)) dx : *!Ç ar.,,Jr (un)nex. qjurJrr^r,j. ?

.un J ç-*<JI "1çr'UJt

9U.,

x - f (x) = 1- #t :x ujr,i>ss§,§i ù,aii .ji-i.,

. limz-1- un = -(c * iTJi""",fl :l5:at'L*J]

f (x) = , +'ff,;r,:r .gluR,r,,ÿ,rr /ur,Jr ,qd(O,i,ï) u*rr+!esu,Êr_C 3lrt q/^r.j (C) Sl:

r.f € R .F.1-i cr":ati.É-r b 9 A ;rç;- gtrs s2 dt ,-p. l

f(x) = x -'J. * ;fi,ff*> = x * z + *. *oo I - co ro / luroçç _ -i. z

.tet).ij Jrr+ ,§. t f iJtJt ïii ôt?ot u,J)l .3

. kalsk" dr.fi t^U+ (d' ) t(d) ù.tit ù*.rU. ù*.*Â:- .p (Ç ),**J ùi ù+ . a

-0,29 <d <-0,28:eeü,t»rÿ-,1r"f (x) = 0 il"GJr oi c,*.5. (d' ),(d.) c," Js Jl qr\, (C,/ ) "-rr

z-rje,esr . €

.(C) ;-r,:: ,ut, çn aQ,f,) :.1;,;.rrôtù-. r

. a zLi:lte (t)"-r.n (A)",ç!ru"t*.-s1.8(c1)t (o)"î*.f'

:ItJ:dJL."{-il

g(x):ex -2x *2:iôtJt RJj,Lir,\gaJt,Jr ùSJ1i. *æ I - @ ,:, iJlrll ,aÇ,*i . t

. t?!,.; Js.? JS: êt R * g 4J1ÀJl cJl+ü ôtjül !r)Jj . 2

.R *g(x) ÀrL:,1ëü-r.3

f (x) =)x + t* 4,isy*lLÀ *br4lex;;,;,,:tçr,t:falrJlïr*,(-.(O,i,i) u.;Ç:"rul,:"eJ.*,J ,it +,1 kli$ Q),§l:

. t-ro a3..ljJlré. -@ r.r, /iffr.ff arç *1. i. I

.r*,raaa,'Jr_,;.limr-1- [tf*l - ]x - f],fimx-1- f(x)."*r.:(D):y -!x * 1 :p;r*Jle(Ç) çUr,--r.r§..Jrÿr1.r')J.e

f' (x) = ff ,r*;J- §s JsJr+r * ùi ù-.i. :.te!»,,iJ,J+,§-tf iltJl üt.-,iiôt*jt êpl .:

. f (a) = 0 .* ]- 1' 0 [...r+.rr 6n d, *e uju,À-cs se n i ù.r. 60 auulr gli;Liirl a3 (Cf)c-r,t:(I).rur usG">.3

. turi.,l +LrA LirL-it ,L:i (Ç) .-*rf oi *. a

.(C1) t (i,)r+t s

eLÀii-glss be.ac,eh(x) = (ax * b)g-*,rRoL *r,JtheltJt xraj.é

. R .r, k(x) = | u,,ts^l-li.L /r;,r**= b,ro un ,